A two-stroke engine includes a scavenging passage opening in a combustion chamber in a scavenging stroke to fill the combustion chamber with a working gas containing a fuel; and a scavenge filling chamber communicating through a communicating port with the scavenging passage and arranged to be filled with a non-working gas in a fuel weight concentration smaller than that of the working gas prior to the scavenging stroke. In the scavenging stroke, the scavenging passage and the scavenging filling chamber are made open in the combustion chamber and the non-working gas in the scavenge filling chamber is forced into the combustion chamber by the working gas inside the scavenging passage through the communicating port to scavenge the combustion chamber.